The ability to improve in speed and accuracy as a result of re-peating some task is an important hallmark of intelligent bio-logical systems. Although gradual behavioural improvementsfrom practice have been modelled in spiking neural networks,few such models have attempted to explain cognitive devel-opment of a task as complex as addition. In this work, wemodel the progression from a counting-based strategy for ad-dition to a recall-based strategy. The model consists of twonetworks working in parallel: a slower basal ganglia loop, anda faster cortical network. The slow network methodically com-putes the count from one digit given another, correspondingto the addition of two digits, while the fast network gradually“memorizes” the output from the slow network. The faster net-work eventually learns how to add the same digits that initiallydrove the behaviour of the slower network. Performance ofthis model is demonstrated by simulating a fully spiking neu-ral network that includes basal ganglia, thalamus and variouscortical areas. Consequently, the model incorporates variousneuroanatomical data, in terms of brain areas used for calcula-tion and makes psychologically testable predictions related tofrequency of rehearsal. Furthermore, the model replicates de-velopmental progression through addition strategies in termsof reaction times and accuracy, and naturally explains observedsymptoms of dyscalculia.

In this paper, we present a spiking neural model of life spaninference. Through this model, we explore the biologicalplausibility of performing Bayesian computations in the brain.Specifically, we address the issue of representing probabil-ity distributions using neural circuits and combining them inmeaningful ways to perform inference. We show that applyingthese methods to the life span inference task matches humanperformance on this task better than an ideal Bayesian modeldue to the use of neuron tuning curves. We also describe po-tential ways in which humans might be generating the priorsneeded for this inference. This provides an initial step towardsbetter understanding how Bayesian computations may be im-plemented in a biologically plausible neural network.

Winner-take-all (WTA) mechanisms are an important compo-nent of many cognitive models. For example, they are oftenused to decide between multiple choices or to selectively di-rect attention. Here we compare two biologically plausible,spiking neural WTA mechanisms. We first provide a novelspiking implementation of the well-known leaky, competingaccumulator (LCA) model, by mapping the dynamics onto apopulation-level representation. We then propose a two-layerspiking independent accumulator (IA) model, and compare itsperformance against the LCA network on a variety of WTAbenchmarks. Our findings suggest that while the LCA net-work can rapidly adapt to new winners, the IA network is bet-ter suited for stable decision making in the presence of noise.

We propose a cognitively plausible method for representingand querying spatial relationships in a neural architecture. Thistechnique employs a fractional binding operator that capturescontinuous spatial information in spatial semantic pointers(SSPs). We propose a model that takes an image with severalobjects, parses the image into an SSP memory representation,and answers queries about the objects. We demonstrate thatour model allows us to not only store and extract objects andtheir spatial information, but also perform queries based on lo-cation and in relation to other objects. We show that we canquery images with 2, 3, and 4 objects with relative spatial lo-cations. We also show that the model qualitatively reproducesKosslyn’s famous map experiment.

We present a novel method for constructing neurally imple-mented spatial representations that we show to be useful forbuilding models of spatial cognition. This method representscontinuous (i.e., real-valued) spaces using neurons, and iden-tifies a set of operations for manipulating these representa-tions. Specifically, we use “fractional binding” to construct“spatial semantic pointers” (SSPs) that we use to generate andmanipulate representations of spatial maps encoding the posi-tions of objects. We show how these representations can betransformed to answer queries about the location and identitiesof objects, move the relative or global position of items, andanswer queries about regions of space, among other things.We demonstrate that the neural implementation in spiking net-works of SSPs have similar accuracy and capacity as the math-ematical ideal.

Keeping track of time is essential for everyday behavior. Theoretical models have proposed a wide variety of neural processes that could tell time, but it is unclear which ones the brain actually uses. Low-level neural models are specific, but rarely explicate how cognitive processes, such as attention and memory, modulate prospective and retrospective timing. Here we develop a neurocomputational model of prospective and retrospective timing, using a spiking recurrent neural network. The model captures behavior of individual spiking neurons and population dynamics when producing and perceiving time intervals, thus bridging low- and high-level phenomena. When interrupting events are introduced, the model delays responding in a similar way to pigeons and rats. Crucially, the model also explains why attending incoming stimuli decreases prospective estimates and increases retrospective estimates of time. In sum, our model offers a neurocomputational account of prospective and retrospective timing, from low-level neural dynamics to high-level cognition.